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Constructing quantum many-body scars from weak Hilbert space fragmentation

Fan Yang, Matteo Magoni, and Hannes Pichler

Phys. Rev. B 113, 174307 – Published 18 May, 2026

DOI: https://doi.org/10.1103/cpt2-kqdy

Abstract

Quantum many-body scars (QMBS) are exotic many-body states that exhibit anomalous nonthermal behavior in an otherwise ergodic system. In this work, we demonstrate a simple, scalable, and intuitive construction of QMBS in a kinetically constrained quantum model exhibiting weak Hilbert space fragmentation. We show that exact QMBS can be constructed by injecting a quasiparticle that partially activates the frozen regions in the lattice. Meanwhile, the inelastic collision between multiple quasiparticles allows for the construction of approximate scars, whose damping is governed by an emergent two-body loss. Our findings establish direct connections between quantum many-body scarring and Hilbert space fragmentation, paving the way for systematically constructing exact and approximate QMBS with nontrivial spatial connectivity. The proposed model can be readily implemented in neutral-atom quantum simulators aided by strong Rydberg interactions.

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References (85)

  1. L. D'Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016).
  2. F. Borgonovi, F. M. Izrailev, L. F. Santos, and V. G. Zelevinsky, Quantum chaos and thermalization in isolated systems of interacting particles, Phys. Rep. 626, 1 (2016).
  3. C. Gogolin and J. Eisert, Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems, Rep. Prog. Phys. 79, 056001 (2016).
  4. M. Serbyn, D. A. Abanin, and Z. Papić, Quantum many-body scars and weak breaking of ergodicity, Nat. Phys. 17, 675 (2021).
  5. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, et al., Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  6. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Weak ergodicity breaking from quantum many-body scars, Nat. Phys. 14, 745 (2018).
  7. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations, Phys. Rev. B 98, 155134 (2018).
  8. W. W. Ho, S. Choi, H. Pichler, and M. D. Lukin, Periodic orbits, entanglement, and quantum many-body scars in constrained models: Matrix product state approach, Phys. Rev. Lett. 122, 040603 (2019).
  9. T. Iadecola, M. Schecter, and S. Xu, Quantum many-body scars from magnon condensation, Phys. Rev. B 100, 184312 (2019).
  10. V. Khemani, C. R. Laumann, and A. Chandran, Signatures of integrability in the dynamics of Rydberg-blockaded chains, Phys. Rev. B 99, 161101(R) (2019).
  11. C.-J. Lin and O. I. Motrunich, Exact quantum many-body scar states in the Rydberg-blockaded atom chain, Phys. Rev. Lett. 122, 173401 (2019).
  12. S. Choi, C. J. Turner, H. Pichler, W. W. Ho, A. A. Michailidis, Z. Papić, M. Serbyn, M. D. Lukin, and D. A. Abanin, Emergent SU(2) dynamics and perfect quantum many-body scars, Phys. Rev. Lett. 122, 220603 (2019).
  13. K. Bull, J.-Y. Desaules, and Z. Papić, Quantum scars as embeddings of weakly broken Lie algebra representations, Phys. Rev. B 101, 165139 (2020).
  14. H. Zhao, J. Vovrosh, F. Mintert, and J. Knolle, Quantum many-body scars in optical lattices, Phys. Rev. Lett. 124, 160604 (2020).
  15. C. J. Turner, J.-Y. Desaules, K. Bull, and Z. Papić, Correspondence principle for many-body scars in ultracold Rydberg atoms, Phys. Rev. X 11, 021021 (2021).
  16. B. Mukherjee, S. Nandy, A. Sen, D. Sen, and K. Sengupta, Collapse and revival of quantum many-body scars via Floquet engineering, Phys. Rev. B 101, 245107 (2020).
  17. B. van Voorden, J. Minář, and K. Schoutens, Quantum many-body scars in transverse field Ising ladders and beyond, Phys. Rev. B 101, 220305(R) (2020).
  18. D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Semeghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, et al., Controlling quantum many-body dynamics in driven Rydberg atom arrays, Science 371, 1355 (2021).
  19. F. M. Surace, M. Votto, E. G. Lazo, A. Silva, M. Dalmonte, and G. Giudici, Exact many-body scars and their stability in constrained quantum chains, Phys. Rev. B 103, 104302 (2021).
  20. J. Li, G. Giudici, and H. Pichler, Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two- and three-dimensional lattices, Phys. Rev. Res. 6, 023146 (2024).
  21. G. Giudici, F. M. Surace, and H. Pichler, Unraveling PXP many-body scars through Floquet dynamics, Phys. Rev. Lett. 133, 190404 (2024).
  22. A. Lerose, T. Parolini, R. Fazio, D. A. Abanin, and S. Pappalardi, Theory of robust quantum many-body scars in long-range interacting systems, Phys. Rev. X 15, 011020 (2025).
  23. D. K. Mark, C.-J. Lin, and O. I. Motrunich, Unified structure for exact towers of scar states in the Affleck-Kennedy-Lieb-Tasaki and other models, Phys. Rev. B 101, 195131 (2020).
  24. S. Moudgalya, N. Regnault, and B. A. Bernevig, η-pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars, Phys. Rev. B 102, 085140 (2020).
  25. N. O'Dea, F. Burnell, A. Chandran, and V. Khemani, From tunnels to towers: Quantum scars from Lie algebras and q-deformed Lie algebras, Phys. Rev. Res. 2, 043305 (2020).
  26. K. Pakrouski, P. N. Pallegar, F. K. Popov, and I. R. Klebanov, Many-body scars as a group invariant sector of Hilbert space, Phys. Rev. Lett. 125, 230602 (2020).
  27. J. Ren, C. Liang, and C. Fang, Quasisymmetry groups and many-body scar dynamics, Phys. Rev. Lett. 126, 120604 (2021).
  28. S. Moudgalya, N. Regnault, and B. A. Bernevig, Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis, Phys. Rev. B 98, 235156 (2018).
  29. M. Schecter and T. Iadecola, Weak ergodicity breaking and quantum many-body scars in spin-1 XY magnets, Phys. Rev. Lett. 123, 147201 (2019).
  30. N. Shiraishi and T. Mori, Systematic construction of counterexamples to the eigenstate thermalization hypothesis, Phys. Rev. Lett. 119, 030601 (2017).
  31. S. Ok, K. Choo, C. Mudry, C. Castelnovo, C. Chamon, and T. Neupert, Topological many-body scar states in dimensions one, two, and three, Phys. Rev. Res. 1, 033144 (2019).
  32. Y. Kuno, T. Mizoguchi, and Y. Hatsugai, Flat band quantum scar, Phys. Rev. B 102, 241115(R) (2020).
  33. K. Omiya and M. Müller, Quantum many-body scars in bipartite Rydberg arrays originating from hidden projector embedding, Phys. Rev. A 107, 023318 (2023).
  34. V. Khemani, M. Hermele, and R. Nandkishore, Localization from Hilbert space shattering: From theory to physical realizations, Phys. Rev. B 101, 174204 (2020).
  35. S. Moudgalya, B. A. Bernevig, and N. Regnault, Quantum many-body scars and Hilbert space fragmentation: A review of exact results, Rep. Prog. Phys. 85, 086501 (2022).
  36. A. Chandran, T. Iadecola, V. Khemani, and R. Moessner, Quantum many-body scars: A quasiparticle perspective, Annu. Rev. Condens. Matter Phys. 14, 443 (2023).
  37. S. Pai, M. Pretko, and R. M. Nandkishore, Localization in fractonic random circuits, Phys. Rev. X 9, 021003 (2019).
  38. G. De Tomasi, D. Hetterich, P. Sala, and F. Pollmann, Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization, Phys. Rev. B 100, 214313 (2019).
  39. P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Pollmann, Ergodicity breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians, Phys. Rev. X 10, 011047 (2020).
  40. S. Pai and M. Pretko, Fractons from confinement in one dimension, Phys. Rev. Res. 2, 013094 (2020).
  41. Z.-C. Yang, F. Liu, A. V. Gorshkov, and T. Iadecola, Hilbert-space fragmentation from strict confinement, Phys. Rev. Lett. 124, 207602 (2020).
  42. A. Hudomal, I. Vasić, N. Regnault, and Z. Papić, Quantum scars of bosons with correlated hopping, Commun. Phys. 3, 99 (2020).
  43. S. Moudgalya, A. Prem, R. Nandkishore, N. Regnault, and B. A. Bernevig, Thermalization and its absence within Krylov subspaces of a constrained Hamiltonian, in Memorial Volume for Shoucheng Zhang (World Scientific, 2021), Chap. 7, pp. 147–209.
  44. L. Zadnik and M. Fagotti, The folded spin-1/2 XXZ model: I. Diagonalisation, jamming, and ground state properties, SciPost Phys. Core 4, 010 (2021).
  45. B. Pozsgay, T. Gombor, A. Hutsalyuk, Y. Jiang, L. Pristyák, and E. Vernier, Integrable spin chain with Hilbert space fragmentation and solvable real-time dynamics, Phys. Rev. E 104, 044106 (2021).
  46. C. M. Langlett and S. Xu, Hilbert space fragmentation and exact scars of generalized Fredkin spin chains, Phys. Rev. B 103, L220304 (2021).
  47. S. Moudgalya and O. I. Motrunich, Hilbert space fragmentation and commutant algebras, Phys. Rev. X 12, 011050 (2022).
  48. B. Buča, Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems, Phys. Rev. X 13, 031013 (2023).
  49. F. Yang, H. Yarloo, H.-C. Zhang, K. Mølmer, and A. E. B. Nielsen, Probing Hilbert space fragmentation with strongly interacting Rydberg atoms, Phys. Rev. B 111, 144313 (2025).
  50. A. Morningstar, V. Khemani, and D. A. Huse, Kinetically constrained freezing transition in a dipole-conserving system, Phys. Rev. B 101, 214205 (2020).
  51. G. Francica and L. Dell'Anna, Hilbert space fragmentation in a long-range system, Phys. Rev. B 108, 045127 (2023).
  52. C. Wang and Z.-C. Yang, Freezing transition in the particle-conserving East model, Phys. Rev. B 108, 144308 (2023).
  53. W. J. Eckner, N. Darkwah Oppong, A. Cao, A. W. Young, W. R. Milner, J. M. Robinson, J. Ye, and A. M. Kaufman, Realizing spin squeezing with Rydberg interactions in an optical clock, Nature (London) 621, 734 (2023).
  54. L.-M. Steinert, P. Osterholz, R. Eberhard, L. Festa, N. Lorenz, Z. Chen, A. Trautmann, and C. Gross, Spatially tunable spin interactions in neutral atom arrays, Phys. Rev. Lett. 130, 243001 (2023).
  55. K. Kim, F. Yang, K. Mølmer, and J. Ahn, Realization of an extremely anisotropic Heisenberg magnet in Rydberg atom arrays, Phys. Rev. X 14, 011025 (2024).
  56. See Supplemental Material at http://link.aps.org/supplemental/10.1103/cpt2-kqdy for animations 1–3 showing the string deformation, string tunneling, and string-assisted hopping, respectively.
  57. T.-L. Tan and Y.-P. Huang, Interference-caged quantum many-body scars: The Fock space topological localization and interference zeros, arXiv:2504.07780.
  58. T. Ben-Ami, M. Heyl, and R. Moessner, Many-body cages: Disorder-free glassiness from flat bands in Fock space, and many-body Rabi oscillations, arXiv:2504.13086.
  59. E. Nicolau, M. Ljubotina, and M. Serbyn, Fragmentation, zero modes, and collective bound states in constrained models, PRX Quantum 7, 010352 (2026).
  60. C. Jonay and F. Pollmann, Localized Fock space cages in kinetically constrained models, Phys. Rev. B 113, 134313 (2026).
  61. L. Rosso, A. Biella, J. De Nardis, and L. Mazza, Dynamical theory for one-dimensional fermions with strong two-body losses: Universal non-Hermitian Zeno physics and spin-charge separation, Phys. Rev. A 107, 013303 (2023).
  62. J. Maki, L. Rosso, L. Mazza, and A. Biella, Loss-induced collective mode in one-dimensional Bose gases, Phys. Rev. A 110, 043315 (2024).
  63. B. M. Garraway, Nonperturbative decay of an atomic system in a cavity, Phys. Rev. A 55, 2290 (1997).
  64. I. de Vega and D. Alonso, Dynamics of non-Markovian open quantum systems, Rev. Mod. Phys. 89, 015001 (2017).
  65. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  66. W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, and M. Greiner, A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice, Nature (London) 462, 74 (2009).
  67. R. Landig, L. Hruby, N. Dogra, M. Landini, R. Mottl, T. Donner, and T. Esslinger, Quantum phases from competing short- and long-range interactions in an optical lattice, Nature (London) 532, 476 (2016).
  68. J. B. Balewski, A. T. Krupp, A. Gaj, S. Hofferberth, R. Löw, and T. Pfau, Rydberg dressing: Understanding of collective many-body effects and implications for experiments, New J. Phys. 16, 063012 (2014).
  69. J. Zeiher, R. van Bijnen, P. Schauß, S. Hild, J.-y. Choi, T. Pohl, I. Bloch, and C. Gross, Many-body interferometry of a Rydberg-dressed spin lattice, Nat. Phys. 12, 1095 (2016).
  70. Y.-Y. Jau, A. M. Hankin, T. Keating, I. H. Deutsch, and G. W. Biedermann, Entangling atomic spins with a Rydberg-dressed spin-flip blockade, Nat. Phys. 12, 71 (2016).
  71. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  72. J. A. Hines, S. V. Rajagopal, G. L. Moreau, M. D. Wahrman, N. A. Lewis, O. Marković, and M. Schleier-Smith, Spin squeezing by Rydberg dressing in an array of atomic ensembles, Phys. Rev. Lett. 131, 063401 (2023).
  73. P. Weckesser, K. Srakaew, T. Blatz, D. Wei, D. Adler, S. Agrawal, A. Bohrdt, I. Bloch, and J. Zeiher, Realization of a Rydberg-dressed extended Bose-Hubbard model, Science 390, 849 (2025).
  74. A. Cao, T. L. Yelin, W. J. Eckner, N. D. Oppong, and A. M. Kaufman, Autoionization-enhanced Rydberg dressing by fast contaminant removal, Phys. Rev. Lett. 134, 133201 (2025).
  75. Z. Lan, M. van Horssen, S. Powell, and J. P. Garrahan, Quantum slow relaxation and metastability due to dynamical constraints, Phys. Rev. Lett. 121, 040603 (2018).
  76. S. Gopalakrishnan and B. Zakirov, Facilitated quantum cellular automata as simple models with non-thermal eigenstates and dynamics, Quantum Sci. Technol. 3, 044004 (2018).
  77. M. Magoni, P. P. Mazza, and I. Lesanovsky, Emergent Bloch oscillations in a kinetically constrained Rydberg spin lattice, Phys. Rev. Lett. 126, 103002 (2021).
  78. T. Kohlert, S. Scherg, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, and M. Aidelsburger, Exploring the regime of fragmentation in strongly tilted Fermi-Hubbard chains, Phys. Rev. Lett. 130, 010201 (2023).
  79. L. Zhao, P. R. Datla, W. Tian, M. M. Aliyu, and H. Loh, Observation of quantum thermalization restricted to Hilbert space fragments and Z2k scars, Phys. Rev. X 15, 011035 (2025).
  80. P. R. Datla, L. Zhao, W. W. Ho, N. Klco, and H. Loh, Statistical localization in a Rydberg simulator of U(1) lattice gauge theory, Nat. Phys. 22, 355 (2026).
  81. K. Lee, A. Pal, and H. J. Changlani, Frustration-induced emergent Hilbert space fragmentation, Phys. Rev. B 103, 235133 (2021).
  82. D. Adler, D. Wei, M. Will, K. Srakaew, S. Agrawal, P. Weckesser, R. Moessner, F. Pollmann, I. Bloch, and J. Zeiher, Observation of Hilbert space fragmentation and fractonic excitations in 2D, Nature (London) 636, 80 (2024).
  83. Y. H. Kwan, P. H. Wilhelm, S. Biswas, and S. A. Parameswaran, Minimal Hubbard models of maximal Hilbert space fragmentation, Phys. Rev. Lett. 134, 010411 (2025).
  84. B. Buča, A. Purkayastha, G. Guarnieri, M. T. Mitchison, D. Jaksch, and J. Goold, Quantum many-body attractors, arXiv:2008.11166.
  85. P. M. Harrington, E. J. Mueller, and K. W. Murch, Engineered dissipation for quantum information science, Nat. Rev. Phys. 4, 660 (2022).

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